Problem: Simplify the following expression: $ r = \dfrac{5}{8} + \dfrac{-10k - 9}{3} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{5}{8} \times \dfrac{3}{3} = \dfrac{15}{24} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-10k - 9}{3} \times \dfrac{8}{8} = \dfrac{-80k - 72}{24} $ Therefore $ r = \dfrac{15}{24} + \dfrac{-80k - 72}{24} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{15 - 80k - 72}{24} $ $r = \dfrac{-80k - 57}{24}$